Identifying Knots within a List: Difference between revisions
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{{Startup Note}} |
{{Startup Note}} |
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<!--$$Import["http://katlas.org/wiki/IdentifyWithin.m&action=raw"];$$ |
<!--$$Import["http://katlas.org/wiki/IdentifyWithin.m&action=raw"];$$--> |
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<!--Robot Land, no human edits to "END"--> |
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{{In| |
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n = 2 | |
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in = <nowiki>Import["http://katlas.org/wiki/IdentifyWithin.m&action=raw"];</nowiki>}} |
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<!--END--> |
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<!--$$SubLink[pd_PD, js_List] := Module[ |
<!--$$SubLink[pd_PD, js_List] := Module[ |
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]; |
]; |
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SubLink[pd_PD, j_] := SubLink[pd, {j}]; |
SubLink[pd_PD, j_] := SubLink[pd, {j}]; |
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SubLink[L_, js_] := SubLink[PD[L], js];$$--> |
SubLink[L_, js_] := SubLink[PD[L], js];$$--> |
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<!--Robot Land, no human edits to "END"--> |
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{{In| |
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n = 3 | |
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in = <nowiki>SubLink[pd_PD, js_List] := Module[ |
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{k, t0, t, t1, t2, S, P}, |
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t0 = Flatten[List @@@ Skeleton[pd][[js]]]; |
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t = pd /. x_X :> Select[x, MemberQ[t0, #] &]; |
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t = DeleteCases[t, X[]]; |
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k = 1; |
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While[ |
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k <= Length[t], |
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If[ Length[t[[k]]] < 4, |
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t = Delete[t, k] /. (Rule @@ t[[k]]), ++k]; |
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]; |
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t1 = List @@ Union @@ t; |
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t2 = Thread[(t1) -> Range[Length[t1]]]; |
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S = t /. t2; |
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P = If[S != PD[] && Length[S] >= 3, S, PD[Knot[0, 1]], S] |
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]; |
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SubLink[pd_PD, j_] := SubLink[pd, {j}]; |
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SubLink[L_, js_] := SubLink[PD[L], js];</nowiki>}} |
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<!--END--> |
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<!--$$IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]$$--> |
<!--$$IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]$$--> |
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<!--Robot Land, no human edits to "END"--> |
<!--Robot Land, no human edits to "END"--> |
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{{InOut| |
{{InOut| |
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n = |
n = 4 | |
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in = <nowiki>IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]</nowiki> | |
in = <nowiki>IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]</nowiki> | |
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out= <nowiki>{Knot[5, 2]}</nowiki>}} |
out= <nowiki>{Knot[5, 2]}</nowiki>}} |
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Revision as of 20:16, 18 November 2007
IdentifyWithin[L,H], whose code is available here, returns those elements from the list of knots , whose invariant matches that of the knot . It can also recognize mirrors and connected sums of the knots in the list. Its options include turning off (on) the search for connected sums with ConnectedSum->False (True) and choosing the invariants to be used in identification by selecting, for example, Invariants->{Jones[#][q]&, HOMFLYPT[#][a,z]&}.
IdentifyWithin can be used together with SubLink to determine the components of a link. For the second component of link L11n150, for instance, we get:
(For In[1] see Setup)
In[2]:=
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Import["http://katlas.org/wiki/IdentifyWithin.m&action=raw"];
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In[3]:=
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SubLink[pd_PD, js_List] := Module[
{k, t0, t, t1, t2, S, P},
t0 = Flatten[List @@@ Skeleton[pd][[js]]];
t = pd /. x_X :> Select[x, MemberQ[t0, #] &];
t = DeleteCases[t, X[]];
k = 1;
While[
k <= Length[t],
If[ Length[t[[k]]] < 4,
t = Delete[t, k] /. (Rule @@ t[[k]]), ++k];
];
t1 = List @@ Union @@ t;
t2 = Thread[(t1) -> Range[Length[t1]]];
S = t /. t2;
P = If[S != PD[] && Length[S] >= 3, S, PD[Knot[0, 1]], S]
];
SubLink[pd_PD, j_] := SubLink[pd, {j}];
SubLink[L_, js_] := SubLink[PD[L], js];
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In[4]:=
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IdentifyWithin[SubLink[Link["L11n150"], 2], AllKnots[]]
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Out[4]=
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{Knot[5, 2]}
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 L11n150 |
 5_2 |
Unfortunately, the program does not provide absolute identification when all the used invariants cannot distinguish between two or more different knots. In that case, a list of possible candidates for is returned.
